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We show that the brightest $\approx$ 20 sources in the current BATSE catalog (as measured by the peak rates in 64, 256 and 1024 ms and the four fluences) are not distributed isotropically on the sky and that their mean vector points in a direction near several known indicators of large-scale structure within $z \sim 0.5$. These structure indicators include peaks in the distributions of low redshifts quasars, optical galaxies, IRAS galaxies, and the microwave background dipole moment. The mean vector of the large-scale structure indicators is centered on galactic coordinates $l = 265\deg$ and $b = 40\deg$ and the mean vector of the brightest $\gamma$-ray bursts is centered on $l = 256\deg$ and $b = 42\deg$. (The close agreement is at least in part accidental since the standard error of the means are somewhat greater than the angular separation of the two mean vectors). The statistical significance of the anisotropy itself is, as expected, only marginal with the probability of a chance occurrence being $\sim 0.01 - 0.1$. However, when combined with the probability of an accidental correlation ($\sim$ 0.1) with the large-scale indicators, a physical association is suggested. If real, the absence of a similar correlation in the PVO, Kronus and earlier $\gamma$-ray burst data, which detected the rarer and much brighter homogeneously distributed bursts, would imply that these instruments primarily detected a different population of sources, a possibility already suggested by the absence of cyclotron lines in the BATSE bursts and the different flux distributions. As a test of these speculative results we predict that the mean vector of the $\sim 10\%$ brightest bursts in future BATSE catalogs will point in a direction near to that found here.
